# Wots a spinor?

1. Dec 1, 2004

### jcsd

What mathematically speaking is a spinor? Why isn't it a tensor? I didn't find the mathworld defintion very useful at all as it describes it as a complex column vector which really tells me nothing especially as we usually think of such an object as a tensor!

2. Dec 1, 2004

### zefram_c

A spinor and a tensor are differentiated mathematically by the way they transform under a Lorentz transformation, and by what they mean physically.

Spinor - See http://particle.phys.uvic.ca/~blokland/phys506a/lec10.pdf [Broken] slide 4 for how a spinor transforms across reference frames.

Tensor - See http://farside.ph.utexas.edu/teaching/jk1/lectures/node10.html for how a tensor transforms.

Note that the transformation for a spinor cannot be put in tensor form, so they are different objects. Physically, spinors arise as solutions to the Dirac equation and describe fermions. I *think* tensors describe fields with integer spin (ie the EM field), but I don't know that for certain.

Edit: shouldn't this go in either Linear Algebra or Quantum physics?

Last edited by a moderator: May 1, 2017
3. Dec 1, 2004

### jcsd

So basically they ARE vectors BUT they exist in a different vector space (a two dimensional complex space as opposed to a four dimensional real space which makes sense in some perverse way)?

So if that is true the obvious quetsion is what is the space that spinors 'live' in meant to represent?

4. Dec 1, 2004

5. Dec 1, 2004

### jcsd

aha that wiki definition is much more enlightening then the mathworld definitnion.